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Sheet1 Page 1 <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" http://www.w3.org/TR/html4/loose.dtd> <html> <head> <title>CS231 Spring 2008 Homework 1 Solutions</title> <meta http-equiv="Content-Type" content="text/html <link rel="stylesheet" type="text/css" href="/~cs231/style.css"> <style type="text/css"> ol li { margin-top: 1em </style> </head> <body> <h2>CS231 Spring 2008 Homework 1 Solutions</h2> <ol> <!-- problem 1 --> <li>(10 pts) Show the detailed steps involved in the following base conversions. In each case, solve for X.<br> <ol type="a"> <li>11100111<sub>2</sub> = X<sub>10</sub> <p> <b>X = 231</b><br> (1x2<sup>7</sup> +1x2<sup>6</sup> +1x2<sup>5</sup> +0x2<sup>4</sup> +0x2<sup>3</sup>+1x2<sup>2</sup> +1x2< = 128 + 64 + 32 + 4 + 2 + 1<br> = <b>231<sub>10</sub></b>) </p> </li> <li>457121<sub>8</sub> = X<sub>16</sub> <p> <b>X = 26E51</b><br> (457121<sub>8</sub><br> = 100 101 111 001 010 001<sub>2 </sub><br> = 0010 0101 1110 0101 0001<sub>2</sub><br> = <b>26E51<sub>16</sub></b>) </p> </li> <li>1101.011<sub>2 </sub> = X<sub>10</sub> <p> <b>X = 13.375</b><br> (1x2<sup>3</sup> +1x2<sup>2</sup> +0x2<sup>1</sup> +1x2<sup>0</sup> +0x2<sup>-1</sup> +1x2<sup>-2</sup> +1x2<sup>-3</sup><br> = 8 + 4 + 1 + 0.25 + .125<br> = <b>13.375<sub>10</sub></b>) </p> </li> <li>A7E.F9B<sub>16</sub> = X<sub>8</sub> <p>
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Sheet1 Page 2 <b>X = 7654.5336</b><br> (A7E.F9B<sub>16 </sub><br> = 1010 0111 1110 . 1111 1001 1011<sub>2</sub><br> = 101 001 111 110 . 111 110 011 011<sub>2</sub><br> = <b>5176.7633<sub>8</sub></b>) </p> </li> <li>231<sub>X</sub> = 100010100<sub>2</sub> <p> <b>X = 11</b><br> (100010100<sub>2</sub> = 2<sup>8</sup> + 2<sup>4</sup> + 2<sup>2</sup> = 276<sub>10</sub><br> 231<sub>X</sub> = 2X<sup>2</sup> + 3X + 1<br> So, 2X<sup>2</sup> + 3X + 1 = 276<br> Using quadratic formula, <b>X = 11</b>) </p> </li> </ol> </li> <!-- problem 2 --> <li>(10 pts) Show the detailed steps (i.e. borrowing, carrying) involved in the following arithmetic calculations:<br> <ol type="a"> <li>1101<sub>2</sub> + 101<sub>2</sub> <p> &nbsp &nbsp <u> + 0101 </u><br> &nbsp </p> </li> <li>101011<sub>2</sub> - 10101<sub>2</sub> <p> &nbsp &nbsp <u>- 010101 </u><br> &nbsp </p> </li> <li>101<sub>2</sub> x 1101<sub>2</sub> <p> &nbsp <u>&nbsp &nbsp <u>+&nbsp &nbsp </p> </li> <li>E7<sub>16</sub> x A2<sub>16</sub>
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Sheet1 Page 3 <p> &nbsp <u>&nbsp &nbsp <u>+9060&nbsp &nbsp </p> </li> <li>4B<sub>16</sub> - 2D<sub>16</sub> <p> &nbsp &nbsp <u>- 2D</u><br> <b>&nbsp </p> </li> </ol> </li> <!-- ========== Problem 3 ========== -->
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